A class of structures relates to self-supporting structures configured to expand or collapse, while maintaining their overall shape as they expand or collapse in a synchronized manner. Such structures have been used for diverse applications including architectural uses, public exhibits, and unique folding toys. A basic building block of such structures is a “loop-assembly” that consists of three or more scissor units (described in U.S. Pat. Nos. 4,942,700 and 5,024,031) or polygon-link pairs (described in U.S. Pat. Nos. 6,082,056 and 6,219,974), each consisting of a pair of links that are pinned together at pivots lying near the middle of each link. Such a loop assembly includes a ring of interconnected links that can freely fold and unfold. Exemplary structures and methods for constructing such reversibly expandable truss-structures in a wide variety of shapes are described in the above referenced patents. Structures that transform in size or shape have numerous uses. If one desires to have a portable shelter of some kind, it should package down to a compact bundle (tents being a prime example).